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Structural analysis based dummy derivative selection for differential algebraic equations

McKenzie, Ross and Pryce, John D. 2017. Structural analysis based dummy derivative selection for differential algebraic equations. BIT Numerical Mathematics 57 (2) , pp. 433-462. 10.1007/s10543-016-0642-9

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Abstract

The signature matrix structural analysis method developed by Pryce provides more structural information than the commonly used Pantelides method and applies to differential-algebraic equations (DAEs) of arbitrary order. It is useful to consider how existing methods using the Pantelides algorithm can benefit from such structural analysis. The dummy derivative method is a technique commonly used to solve DAEs that can benefit from such exploitation of underlying DAE structures and information found in the Signature Matrix method. This paper gives a technique to find structurally necessary dummy derivatives and how to use different block triangular forms effectively when performing the dummy derivative method and then provides a brief complexity analysis of the proposed approach. We finish by outlining an approach that can simplify the task of dummy pivoting.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Uncontrolled Keywords: DAEs Numerical Analysis
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
Publisher: Springer Verlag
ISSN: 0006-3835
Funders: The Leverhulme Trust
Date of First Compliant Deposit: 30 May 2017
Date of Acceptance: 8 November 2016
Last Modified: 26 Jul 2019 20:50
URI: http://orca.cf.ac.uk/id/eprint/100978

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